This result agrees with Ref [1]}. The arguments of the hyperbolic functions in QuantumVlasov are large enough that we approximate the function \(F\)  as
\(F\Big (\mathbf {p},E_0f(z),t\rightarrow \infty \Big ) \approx 2 \,e^{\pi \tau \big (2\tau e E_0f(z)-\epsilon -\tilde{\epsilon } \big )}\) 
